Luis Crespo

collaborators

7 papers

math.SG2026

$p$ -adic integrable systems: from biquadratic equations to local models

Luis Crespo, Ãlvaro Pelayo

Let $p$ be a prime number and $n$ a positive integer. The study of normal forms of $p$ -adic analytic integrable systems $F = (f_{1}, \dots, f_{n}) : (M, I ¨ ) \to (Q_{p})^{n}$ is essential…

math.SG2026

Darboux's Theorem in $p$ -adic symplectic geometry

Luis Crespo, Ãlvaro Pelayo

We prove a non Archimedean Darboux's Theorem: any two symplectic forms on a $p$ -adic analytic manifold are locally isomorphic. Understanding local problems such as the existence of…

math.SG2026

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory II

Luis Crespo, Ãlvaro Pelayo

This paper is a sequel to arXiv:2501.14444, in which we shall give proofs of several results stated in arXiv:2501.14444 (Theorems D--L) which, for brevity and clarity, we postponed…

math.SG2026

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I

Luis Crespo, Ãlvaro Pelayo

The local symplectic theory of integrable systems is fundamental to understand their global theory, as well as the behavior near singularities of fundamental models from classical…

math.SG2025

Group actions on $p$ -adic symplectic manifolds

Luis Crespo, Ãlvaro Pelayo

Let $p$ be a prime number. We introduce symplectic actions of $p$ -adic analytic Lie groups on $p$ -adic symplectic manifolds. Then we show that any $p$ -adic symplectic action $G\tim…

math.SG2025

$p$ -adic angular momentum coupling in symplectic geometry

Luis Crespo, Ãlvaro Pelayo

The coupled angular momentum is an integrable system with two degrees of freedom which is fundamental in physics and the theory of integrable systems. It is obtained by coupling tw…

p-adic integrable systems: from biquadratic equations to local models

Darboux's Theorem in p-adic symplectic geometry

p-adic symplectic geometry of integrable systems and Weierstrass-Williamson theory II

p-adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I

Group actions on p-adic symplectic manifolds

p-adic angular momentum coupling in symplectic geometry

$p$ -adic integrable systems: from biquadratic equations to local models

Darboux's Theorem in $p$ -adic symplectic geometry

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory II

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I

Group actions on $p$ -adic symplectic manifolds

$p$ -adic angular momentum coupling in symplectic geometry